We will start by describing the lower-dimensional obstacle problem, for a uniformly elliptic divergence form operator with Lipschitz continuous coefficients and discuss the optimal regularity of the solution. Our main result states that, similarly to what happens for the Laplacian, the variational solution has the optimal interior regularity C^{1,1/2}(O±UM), where M is a codimension one flat manifold which supports the obstacle and divides the domain O into two parts, $O+$ and $O-$. We achieve this by proving some new monotonicity formulas for an appropriate generalization of the celebrated Almgren's frequency functional.